This phase II trial studies how well TPIV100 and sargramostim work in treating patients with HER2 positive, stage II-III breast cancer that has residual disease after chemotherapy prior to surgery. It also studies why some HER2 positive breast cancer patients respond better to chemotherapy in combination with trastuzumab and pertuzumab. TPIV100 is a type of vaccine made from HER2 peptide that may help the body build an effective immune response to kill tumor cells that express HER2. Sargramostim increases the number of white blood cells in the body following chemotherapy for certain types of cancer and is used to alert the immune system. It is not yet known if TPIV100 and sargramostim will work better in treating patients with HER2 positive, stage II-III breast cancer.

The goal of this clinical trial is to evaluate the safety and efficacy of TOS-358 in women with HR+ HER2- metastatic breast cancer whose tumors have a mutation in PIK3CA and who meet all other study enrollment criteria. The main questions it aims to answer are:

1. Phase 1a: what is the maximum tolerated dose and recommended dose for phase 2?
2. Phase 1a: how safe and tolerable is TOS-358 at different dose levels when taken orally once or twice per day?
3. Phase 1b: how safe and effective is TOS-358 when given with standard of care medicines for HR+HER2- metastatic breast cancer (fulvestrant and CDK4/6i)

The primary goal of this study is to evaluate the effectiveness of elacestrant versus standard endocrine therapy in participants with node-positive, Estrogen Receptor-positive (ER+), Human Epidermal Growth Factor-2 negative (HER2-) early breast cancer with high risk of recurrence.

Researchers are looking for new ways to treat types of breast cancer that are both:

* High-risk, which means the cancer may have a higher chance of getting worse or coming back after treatment
* Early-stage, which means the cancer is in the breast or the lymph nodes around the breast The 2 types of breast cancer in this study are triple-negative breast cancer (TNBC) and hormone receptor (HR)-low positive/human epidermal growth factor receptor-2 (HER2) negative breast cancer. These cancers have zero or a low amount of a protein called HER2 and other proteins that attach to the hormones estrogen or progesterone.

Sacituzumab tirumotecan (also known as sac-TMT or MK-2870), the study medicine, is a type of targeted therapy. A targeted therapy is a treatment that works to control how specific types of cancer cells grow and spread.

The main goals of this study are to learn if people who receive sac-TMT, pembrolizumab, and chemotherapy:

* Have fewer cancer cells found in the tumors and lymph nodes removed during surgery compared to those who receive only pembrolizumab and chemotherapy
* Live longer without the cancer growing, spreading, or coming back compared to people who receive only pembrolizumab with chemotherapy